Investors have become increasingly interested in controlling the risk associated with investment portfolios, risk being characterized by an anticipated likely rate of change in the value of the portfolio. Mutual funds, for instance, allow investors to control or minimize risk through diversified asset holdings. Overlooked, however, is the important principle of maintaining a certain level of dollar risk, or absolute risk, over time. Relative risk, or percentage risk, in the stock market, which is characterized by dollar gain or loss divided by initial dollar investment, tends to be fairly constant over long periods of time. Absolute risk, or dollar risk, by contrast, is characterized simply by dollar risk over time.
If an investor simply buys and holds assets in a portfolio, the absolute risk associated with the portfolio will change over time, as the level of the market changes over time. If the market increases, the absolute risk increases, and vice versa. In a sense, the investor is allowing his future bet to be determined by the results of his last bet. Over time, the effect of this skewing of absolute risk is magnified and very significant.
It would be desirable to be able to maintain a portfolio that is time diversified, in the sense that the absolute risk associated with the portfolio stays approximately constant over time. Furthermore, it would be desirable to do so with minimal trading, so as to incur a minimal expense, difficulty, or inconvenience associated with the trading.
The old view of diversification was well expressed in the adage, “don't put all your eggs in one basket.” The modem view advises instead, “don't put your eggs in correlated baskets.” The modem model for diversification, or for overcoming uncertainty, is the mean of a random variable. If the drawings from the variable's frequency distribution are random, then the “standard deviation” of the sample mean varies inversely with the square root of the size of the sample.
The return to the investor's portfolio is a weighted mean of returns to individual investments. But the analogy with the sample mean fails if the individual investment values go up and down together. If individual stocks weren't correlated, there would be little uncertainty about the future value of the S&P 500, or of many mutual funds. If, on the other hand, individual stocks were perfectly correlated, there would be little point in owning such funds.
Because returns on individual stock are correlated, albeit imperfectly, the square-root law doesn't apply. Indeed, there's a limit to how much risk a mutual fund can eliminate. Market returns in different years are generally uncorrelated; if they weren't, investors would use past returns to profitably predict future returns.
For the buy-and-hold investor, the scale of next year's bet is determined by the outcome of last year's bet. In their impact on his “terminal wealth,” which can be, for example, wealth at retirement or some other target point, the individual years multiply. So the additive model of the sample mean doesn't apply.
Yet the fact remains that the investor's terminal wealth is the (algebraic) sum of the gains and losses in the individual year. If, as many finance scholars believe, the risk surrounding the market's rate of return is roughly constant across time (“stationary”) then, when the market level doubles, the risk of dollar gains and losses also doubles.
Unless an investor is rash enough to think he can distinguish beforehand between the good market years and the bad, the investor may want each year to have the same potential dollar impact on his terminal wealth. When the market level doubles, time diversification will require that he sell half his stock portfolio, etc. maintaining constant dollar risk entails a lot of expensive trading. The conventional investor is faced with a dilemma: either incur those draconian trading costs, or give up the benefits of time diversification, as buy-and-hold investors do.
Therefore, there is a need for a method for a method for maintaining an absolute risk level for an investment portfolio while minimizing trading necessary to maintain the absolute risk level.